As of me , i add one more checks as page isn't accidentally carrying noindex or being blocked by robot.txt. and worthy enough to check final url after redirects becoz links look fine but it drag to somewhere unexpected.
I tend to go through the same routine i will test the link to ensure that it works and leads to the proper URL without being interrupted by any odd redirects or attributes i would also want to ensure that the page is crawlable it is nothing fancy but it is all too easy to overlook one of these things.
I would also make sure that the page was indexed, that the link was contextual, that the anchor was natural and that there were no strange issues with canonical or noindex.
honesty, I first check the indexing, canonical, robots, and anchor positioning. I will also look into the source code to find out whether there is anything weird in the link in terms of rel or redirect attribute.
Yeah, I'd check the technical aspect as well. Having a clean URL without a redirect chain with a natural placement in the body of the content is far more preferable than a sitewide/template link.
I usually check for the live link clickable, target URL, anchor text, rel attributes, 200 status, canonical URL. That's generally enough to confirm the links was properly delivered.